Computation of Greeks Using Binomial Tree
Computation of Greeks Using Binomial Tree
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DOI：
10.4236/jmf.2017.73031
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发表时间：
2017-06
期刊：
影响因子：
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通讯作者：
Yoshifumi Muroi;Shintaro Suda
中科院分区：
文献类型：
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作者：
Yoshifumi Muroi;Shintaro Suda
本文提出了一个新的有效算法，计算希腊人的选择使用二叉树。我们还表明，希腊人在这篇文章中介绍的欧洲选项是渐近等价的Malliavin希腊人的离散版本。这一事实使我们能够证明，在连续时间模型中，我们的希腊语收敛于Malliavin希腊语。本文还给出了利用二叉树计算美式期权希腊式的算法。使用二叉树方法计算希腊人有三个优点。首先，数学比使用连续时间Malliavin微积分方法简单得多。其次，我们可以构造一个简单的算法来获得美式期权的希腊式。第三，该算法非常有效，因为可以同时计算价格和希腊语（delta、gamma、vega和rho）。尽管它的重要性，只有少数以前的研究计算希腊的美式期权存在，因为进行灵敏度分析的最佳停止问题是困难的。我们相信，我们的方法将成为一个流行的方法来计算希腊期权。
This paper proposes a new efficient algorithm for the computation of Greeks for options using the binomial tree. We also show that Greeks for European options introduced in this article are asymptotically equivalent to the discrete version of Malliavin Greeks. This fact enables us to show that our Greeks converge to Malliavin Greeks in the continuous time model. The computation algorithm of Greeks for American options using the binomial tree is also given in this article. There are three advantageous points to use binomial tree approach for the computation of Greeks. First, mathematics is much simpler than using the continuous time Malliavin calculus approach. Second, we can construct a simple algorithm to obtain the Greeks for American options. Third, this algorithm is very efficient because one can compute the price and Greeks (delta, gamma, vega, and rho) at once. In spite of its importance, only a few previous studies on the computation of Greeks for American options exist, because performing sensitivity analysis for the optimal stopping problem is difficult. We believe that our method will become one of the popular ways to compute Greeks for options.